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本文通过对谱峰分离的拟合方法所涉及的数学规划问题的研究,提出M个重叠峰分离计算应作为有约束非线性规划问题看待;提出了DRAT(降维-绝对值变换)计算策略,它通过构造线性模型参数的极小化点集并对此进行绝对值变换,使得一个3M+1维有约束规划问题转化成一个等价的2M维无约束规划问题;在此基础上,应用改进Powell方法、BFGS变尺度方法以及二者的偶合方法,成功地在微机上实现了对一些典型的二重叠直至七重叠峰的完全分离。理论分析和实算结果表明,将谱峰分离计算处理成有约束规划问题,可以有效地避免由于峰参数初值估计不当所引起的假收敛;DRAT计算方法,由于考虑了约束的作用并且优化过程不直接涉及峰强参数,因而具有较强的收敛性和很宽的可行初值范围,从而它为各类谱图解析中的重叠峰分离工作提供了一种有效的计算方法。
In this paper, we study the mathematic programming problems involved in the fitting method of spectral peaks, and propose that the calculation of M overlapping peaks should be considered as a constrained nonlinear programming problem. A calculation strategy of DRAT (reduced dimension - absolute value transformation) It constructs a minimization point set of linear model parameters and transforms it by absolute value, so that a 3M + 1-D constrained programming problem can be transformed into an equivalent 2M-dimensional unconstrained programming problem. On this basis, Powell method, BFGS variable-size method and the coupling method of the two methods, successfully completed the complete separation of some typical double overlapping to seven overlapping peaks on a microcomputer. The theoretical analysis and practical results show that the calculation of the peak separation into a constrained programming problem can effectively avoid the false convergence caused by the improper estimation of the initial parameters of the peak parameters. Due to the consideration of the constraint and the optimization process It does not directly involve the peak intensity parameters, so it has a strong convergence and a very wide range of feasible initial values. Therefore, it provides an effective method for the calculation of overlapped peaks in various spectral analysis.